Asymptotics and Singularities in Nonlinear and Geometric Dispersive Equations (08w5058)
One of the obvious goals of the proposed workshop is to bring together a geographically quite diverse collection of researchers with core common interests in global questions for nonlinear dispersive equations. The mathematicians we have in mind are based in east Asia, North America, and Europe, and seem to have relatively few opportunities for close interaction (and the field can suffer somewhat as a result). The opportunity to learn firsthand of our colleagues' latest advances will be a clear benefit of the workshop.
Another goal is to promote more interaction between researchers who approach quite similar problems from somewhat different points-of-view, and with different tools and expertise. Those with disparate backgrounds (for example, in mathematical physics, classical analysis, dynamical systems, applied mathematics, or geometry) might not always learn quickly enough of each others' approaches and techniques, while optimal progress in the field requires timely input from all these angles. To this end, we plan to include some researchers whose background is not necessarily ``pure PDE'': for example, some mathematical physicists, and some somewhat more ``applied'' mathematicians. Similarly, a wide variety of techniques have recently proved fruitful in addressing the problems described above (for example: stability theory, linear estimates, harmonic analysis, Hamiltonian systems, spectral theory, dynamical systems, geometric methods, Liouville theorems, monotonicity properties, formal asymptotics, etc.), and we feel that experts with these various methods do not get sufficient opportunity to intersect. We hope our proposed workshop can help to remedy this.
A third goal is to help ensure some young talent gets and stays involved in the field. To that end, we anticipate allotting around 10 (at least) places for graduate students, postdocs, and new faculty (mostly not yet included on the tentative list below).
Finally, this lively and fast-moving (yet in many ways still wide open) field, which seems to have attracted a ``critical mass'' of quality researchers, seems to be ready for a leap into tackling some of the biggest problems. A good example is moving away from perturbative settings into truly global ones, a move which (in the presence of localized solutions) is only just beginning. We would very much like to see some breakthroughs of this sort emerge from our workshop.